∫0

(ii) Determination of forward interest rates —(A) In general . The forward interest rate function used to derive the discount function is determined as a series of cubic polynomials (referred to as a cubic spline) that have a smooth junction at specified knot points (maturities of 0, 1.5, 3, 7, 15, and 30 years). The requirement that the polynomials have a smooth junction at a knot point is satisfied if the two polynomials that are meeting at the knot have the same value, the same derivative, and the same second derivative at that knot point.

(B) Constraints on the forward interest function . The following three constraints are placed on the forward interest rate function—

( 1 ) The second derivative of the function is set to zero at maturity zero.

( 2 ) The value of the forward interest rate function at and after 30 years is constrained to equal its average value from 15 to 30 years.

( 3 ) The derivative of the forward interest rate function is set to zero at maturity 30 years. (iii) Parameters for daily bond price model —(A) B-spline coefficients . The assumed cubic spline for the forward interest rate function can be described as a linear combination of B-splines, with five parameters, which are determined taking into account the two coefficients for the bond-quality adjustment variables

described in paragraphs (d)(2)(iii)(B) and (C) of this section and the coefficient for the hump adjustment variable described in paragraph (d)(2)(iii)(D) of this section. The five parameters and three coefficients are determined using the bond data weighted as described in paragraph (d)(2) (iv) of this section. After this weighting of the bond data, the five parameters and three coefficients are chosen to minimize the sum of the squared differences between the bid price for each of the bonds (or ask price for commercial paper) and the price estimated for each of those bonds determined using the specified parameters and coefficients, and taking into account the bond’s coupon rate, number of years until maturity, and rating.

(B) Adjustment factor for share of bonds that are AA-rated . The first adjustment variable is based on the proportion of bonds that are rated AA within the universe of bonds in the data set that are rated AA or AAA, weighted by par value. In the case of an AAA-rated bond the adjustment variable described in this paragraph (d)(2)(iii)(B) is equal to the product of the proportion described in the preceding sentence and the number of years until maturity for the bond. In the case of an AA-rated bond the adjustment variable described in this paragraph (d)(2)(iii)(B) is equal to the product of (1- that proportion) and the number of years until maturity for the bond. In the case of an A‑rated bond, the adjustment variable described in this paragraph (d)(2)(iii)(B) is set to 0.

(C) Adjustment factor for share of bonds that are A‑rated . The second adjustment variable is based on the proportion of bonds rated A within the universe of bonds in the data set, weighted by par value. In the case of an AAA-rated bond or an AA-rated bond, the adjustment variable described in this paragraph (d)(2)(iii)(C) is equal to the product of the proportion described in the preceding sentence and the number of years until maturity for the bond. In the case of an A-rated bond the adjustment variable described in this paragraph (d)(2)(iii)(C) is equal to the product of (1- that proportion) and the number of years until maturity for the bond.

(D) Hump adjustment variable . The hump adjustment variable is a mathematical function that is a cubic spline in the interval from 10 years maturity through

Bulletin No. 2023–30 373 July 24, 2023

(D) Bonds having variable coupon rates;

(E) Convertible bonds; (F) Bonds issued by a government-sponsored enterprise (such as the Federal National Mortgage Association);

(G) Asset-backed bonds; (H) Callable bonds unless the call feature is make-whole or the call feature is exercisable only during the last year before maturity;

(I) Putable bonds; (J) Bonds with sinking funds; and

(K) Bonds with a par amount outstanding below $250 million for the day for which the daily yield curve is constructed.

(iii) Durations equal to or below a ½ year . The data for durations equal to or below a ½ year that is used to construct the daily corporate bond yield curve consists of AA financial and AA nonfinancial commercial paper rates, as reported by the Federal Reserve Board.

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(h) Applicability date of regulations . This section applies to months that begin more

than 15 days after the date final regulations issued pursuant to these proposed regulations are published in the Federal Register . For rules that apply for earlier periods, see §1.430(h)(2)-1, as it appeared in the April 1, 2022, edition of 26 CFR part 1.

Douglas W. O’Donnell, Deputy Commissioner for Services

and Enforcement .

(Filed by the Office of the Federal Register June 22, 2023, 8:45 a.m., and published in the issue of the Federal Register for June 23, 2023, 88 FR 41047)

July 24, 2023 374 Bulletin No. 2023–30